# Fractions

## Objective

Compare fractions with the same numerators by reasoning about the size of their units. Record the results of comparisons with the symbols >, =, or <.

## Common Core Standards

### Core Standards

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• 3.NF.A.3.D — Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

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• 2.MD.A.2

## Criteria for Success

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1. Compare fractions with the same numerator by using the understanding that when the denominator is larger, the pieces are smaller, and thus when comparing fractions with the same numerators, the fraction with a denominator that is high in value is smaller than a fraction with a denominator that is low in value (MP.2).
2. Record the results of comparisons with the symbols >, =, or <.
3. Justify comparisons of fractions with the same numerator using the reasoning above and/or using an area model or number line (MP.3, MP.5).

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### Problem 1

LaTonya has 2 equal-sized candy bars. She cut the first candy bar into fourths after lunch and eats three pieces. Later, she cut the second candy bar into sixths after dinner and eats three pieces. Did LaTonya eat the same amount of the candy bar and second candy bar? If not, did she eat more after lunch or after dinner? Show or explain how you know.

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#### References

EngageNY Mathematics Grade 3 Mathematics > Module 5 > Topic F > Lesson 28Concept Development

Grade 3 Mathematics > Module 5 > Topic F > Lesson 28 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

1. Who correctly compares the numbers $\frac{2}{3}$ and $\frac{2}{5}$?

i.  Ben said that $\frac{2}{3}$ is greater than $\frac{2}{5}$.

ii.  Lee said that $\frac{2}{3}$ is equal to $\frac{2}{5}$.

iii.  Mia said that $\frac{2}{3}$ is less than $\frac{2}{5}$.

1. Compare $\frac{2}{3}$ and $\frac{2}{5}$ using symbols:

$\frac{2}{3}$ _____ $\frac{2}{5}$

1. Choose the two pictures that best compare $\frac{2}{3}$ and $\frac{2}{5}$.

#### Guiding Questions

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#### References

Illustrative Mathematics Fraction Comparisons with Pictures, Assessment Variation

Fraction Comparisons with Pictures, Assessment Variation, accessed on March 19, 2019, 11:11 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

### Problem 3

1. Choose each statement that is true.

i.  $\frac{9}{8}$ is greater than $\frac{9}{4}$.

ii.  $\frac{9}{4}$ is greater than $\frac{9}{8}$.

iii.  $\frac{9}{8}>\frac{9}{4}.$

iv.  $\frac{9}{8}<\frac{9}{4}.$

v.  $\frac{9}{4}>\frac{9}{8}$.

vi.  $\frac{9}{4}<\frac{9}{8}.$

vii.  None of these.

1. $\frac{9}{8}$ and $\frac{9}{4}$ are shown on the number line. Which is correct?

i.

ii.

iii. Neither of these.

#### Guiding Questions

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#### References

Illustrative Mathematics Comparing Fractions with the Same Numerators, Assessment Variation

Comparing Fractions with the Same Numerators, Assessment Variation, accessed on March 19, 2019, 11:12 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

## Problem Set & Homework

#### Discussion of Problem Set

• If you only know the number of shaded parts, can you tell if fractions are equivalent? Why or why not?
• Look at the models in #1─4. When comparing fractions, why is it so important that the wholes are the same size?
• Tell a partner how you used the models in #1─4 to determine greater than, less than, or equal to.
• Explain a general strategy for comparing fractions with the same numerators.

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### Problem 1

Fill in the blank to make the statement true.

$\frac{3}{4}>\frac{3}{\square}$

### Problem 2

Two fractions are shown below.

$\frac{2}{8} \hspace{1cm} \frac{2}{3}$

1. Write a number sentence to compare $\frac{2}{8}$ and $\frac{2}{3}$. Use <, >, or = in your number sentence.
2. Draw a model that shows your number sentence is correct.

#### References

Massachusetts Department of Elementary and Secondary Education Spring 2014 Grade 3 Mathematics TestQuestion #11

Spring 2014 Grade 3 Mathematics Test is made available by the Massachusetts Department of Elementary and Secondary Education. © 2017 Commonwealth of Massachusetts. Accessed Sept. 25, 2018, 4:25 p.m..

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